Basic Math Examples

$\frac{\log (3)}{\log_{n} (3)}$

Step 1

Rewrite $\log_{n} (3)$ using the change of base formula.

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Step 1.1

The change of base rule can be used if $a$ and $b$ are greater than $0$ and not equal to $1$ , and $x$ is greater than $0$ .

$\frac{\log (3)}{\log_{a} (x) = \frac{\log_{b} (x)}{\log_{b} (a)}}$

Step 1.2

Substitute in values for the variables in the change of base formula, using $b = 10$ .

$\frac{\log (3)}{\frac{\log (3)}{\log (n)}}$

Step 2

Multiply the numerator by the reciprocal of the denominator.

$\log (3) \frac{\log (n)}{\log (3)}$

Step 3

Cancel the common factor of $\log (3)$ .

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Step 3.1

Cancel the common factor.

$\log (3) \frac{\log (n)}{\log (3)}$

Step 3.2

Rewrite the expression.

$\log (n)$